Here's just a little idea I had for a custom die. Originally, I imagined a d6 with six pips on each face, but only 1-6 filled. That way, you could pull two sets of information from a single result.
Unfortunately, that means one face would have 0 filled pips and 6 empty pips and there wouldn't be enough faces for a mirrored counterpart.
So I knocked off one pip on each face. Now I could start with 0 filled 5 empty, incrementally increase the filled pips on each face up to 5 filled 0 empty. I don't know what you'd do with a die like this, but it's an interesting source of data, easily based on binary states in an RPG for example:
"Roll 2dM. If the scene takes place in the day, check the empty pips. If the scene takes place at night, check the filled pips."
I'm sure you can think of something better though. What would you do with these?